PROPAGATING FRONTS AND THE CENTER MANIFOLD THEOREM

We prove the existence of propagating front solutions for the Swift-Hohenberg equation (SH). Using the center manifold theorem we reduce the problem to a two dimensional system of ordinary differential equations. They describe stationary solutions and front solutions of the partial differential equation (SH). We identify the well-known "amplitude equation" as the lowest order approximation to the equation of motion on the center manifold.